B4A=true Group=Default Group ModulesStructureVersion=1 Type=Class Version=8.3 @EndOfDesignText@ ' Conversions between Lat/Lon and local grid systems and supporting utilities. ' TRF = Terrestrial Reference Frame. Grid = Cartesian Grid. Sub Class_Globals Type LatLon (Latitude, Longitude As Double) ' Latitude/Longitude reference in degrees Type GridRef (Easting, Northing As Double) ' Cartesian grid reference in metres Dim PI As Double = 3.1415926535897932385 Dim RADIAN As Double = 2.0 * PI / 360 End Sub Public Sub Initialize End Sub Private Sub TRFtoGrid(Degrees As LatLon, a As Double, b As Double, N0 As Int, E0 As Int, F0 As Double, phi0 As Double, lambda0 As Double) As GridRef ' TRF Lat/Lon To Grid East/North by Transverse Mercator projection. ' is latitude - negative if south of equator (all angles in radians) ' is longitude - negative if west of prime meridian ' And are major and minor axes of ellipsoid ' And are easting and northing of grid origin ' is scale factor on central meridian of grid ' And are latitude and longitude of grid origin ' And are easting and northing of converted grid reference Dim Phi, Lambda As Double Dim n, n2, n3, e2, nu, rho, eta2 As Double ' Geometric terms Dim M, I, II, III, IIIa, IV, V, VI As Double ' Intermediate terms Dim sin1, sin2, cos1, cos2, cos3, cos5 As Double Dim tan1, tan2, tan4 As Double ' Trig's of and their powers Dim phidiff, phi2diff, phi3diff As Double ' (Phi - phi0), (Phi + phi0) and Dim phisum, phi2sum, phi3sum As Double ' their multiples Dim L, L2, L3, L4, L5, L6 As Double ' (Lambda - lambda0) And its powers Dim x As Double ' Temporary intermediate value term Dim result As GridRef Phi = Degrees.Latitude * RADIAN ' Convert to radian measure Lambda = Degrees.Longitude * RADIAN n = (a - b) / (a + b) n2 = n * n n3 = n2 * n e2 = (a * a - b * b) / (a * a) ' Eccentricity squared value ' Calculate trigonometric factors sin1 = Sin(Phi) : cos1 = Cos(Phi) sin2 = sin1 * sin1 cos2 = cos1 * cos1 : cos3 = cos2 * cos1 : cos5 = cos3 * cos2 tan1 = sin1 / cos1 : tan2 = tan1 * tan1 : tan4 = tan2 * tan2 x = (1 - e2 * sin2) nu = a * F0 / Sqrt(x) rho = a * F0 * ( 1 - e2) / Sqrt(x * x * x) eta2 = nu / rho - 1.0 phidiff = (Phi - phi0) : phi2diff = phidiff + phidiff phi3diff = phi2diff + phidiff phisum = (Phi + phi0) : phi2sum = phisum + phisum phi3sum = phi2sum + phisum M = b*F0 * ( (1 + n + 1.25 * (n2 + n3)) * phidiff _ - (3 * (n + n2) + 2.625 * n3) * Sin(phidiff) * Cos (phisum) _ + 1.875 * (n2 + n3) * Sin(phi2diff) * Cos(phi2sum) _ - 35/24 * n3 * Sin(phi3diff) * Cos(phi3sum)) I = M + N0 x = nu * sin1 II = x * cos1 * 0.5 III = x * cos3 * (5 - tan2 + 9*eta2) / 24 IIIa = x * cos5 * (61 - 58*tan2 + tan4) / 720 IV = nu * cos1 V = nu * cos3 * (nu / rho - tan2) / 6 VI = nu * cos5 * (5 - 18*tan2 + tan4 + 14*eta2 - 58*tan2*eta2) / 120 L = (Lambda - lambda0) L2 = L * L : L3 = L2 * L : L4 = L3 * L : L5 = L4 * L : L6 = L5 * L result.Northing = I + II * L2 + III * L4 + IIIa * L6 result.Easting = E0 + IV * L + V * L3 + VI * L5 Return result End Sub Private Sub GridToTRF(Position As GridRef, a As Double, b As Double, N0 As Double, E0 As Double, F0 As Double, phi0 As Double, lambda0 As Double) As LatLon ' Grid East/North To TRF Lat/Lon by Inverse Transverse Mercator projection ' And are easting and northing of converted grid reference. ' And are major and minor axes of ellipsoid. ' And are easting and northing of grid origin. ' Is scale factor on central meridian of grid. ' And are latitude and longitude of grid origin. ' Is latitude - negative If south of equator (all in radians). ' Is longitude - negative If west of prime meridian. Dim East, North As Double Dim n, n2, n3, e2, rho, eta2 As Double ' Geometric terms Dim nu, nu2, nu3, nu5, nu7 As Double Dim M, VII, VIII, IX, X, XI, XII, XIIA As Double ' Intermediate terms Dim phi1 As Double ' in OS booklet Dim sin1, sin2, cos1, sec As Double Dim tan1, tan2, tan4, tan6 As Double ' Trig's of and their powers Dim phidiff, phi2diff, phi3diff As Double ' (phi1 - phi0), (phi1 + phi0) and Dim phisum, phi2sum, phi3sum As Double ' their multiples Dim Ediff, Ediff2 As Double ' (E - E0) and its square Dim z As Double ' Temporary intermediate value term Dim result As LatLon East = Position.Easting North = Position.Northing n = (a - b) / (a + b) ' Calculate 'M' constant terms n2 = n * n n3 = n2 * n e2 = (a * a - b * b) / (a * a) ' Eccentricity squared value z = 1 / a /F0 phi1 = (North - N0) * z + phi0 Do Until (Abs(North - N0 - M) < 0.001) phidiff = (phi1 - phi0) : phi2diff = phidiff + phidiff phi3diff = phi2diff + phidiff phisum = (phi1 + phi0) : phi2sum = phisum + phisum phi3sum = phi2sum + phisum M = b * F0 * ((1 + n + 1.25 * (n2 + n3)) * phidiff _ - (3 * (n + n2) + 2.625 * n3) * Sin(phidiff) * Cos (phisum) _ + 1.875 * (n2 + n3) * Sin(phi2diff) * Cos(phi2sum) _ - 35/24 * n3 * Sin(phi3diff) * Cos(phi3sum)) phi1 = (North - N0 - M) * z + phi1 Loop ' Now that has been determined calculate trigonometric factors sin1 = Sin(phi1) : cos1 = Cos(phi1) sin2 = sin1 * sin1 : sec = 1 / cos1 tan1 = sin1 / cos1 : tan2 = tan1 * tan1 : tan4 = tan2 * tan2 tan6 = tan2 * tan4 z = (1 - e2 * sin2) nu = a * F0 / Sqrt(z) nu2 = nu * nu : nu3 = nu2 * nu : nu5 = nu2 * nu3 : nu7 = nu5 * nu2 rho = a * F0 * ( 1 - e2) / Sqrt(z * z * z) eta2 = nu / rho - 1.0 VII = tan1 / rho / nu * 0.5 VIII = tan1 / rho / nu3 * (5 + 3 * tan2 + eta2 - 9 * tan2 * eta2) / 24 IX = tan1 / rho / nu5 * (61 + 90 * tan2 + 45 * tan4) / 720 X = sec / nu XI = sec / nu3 * (nu / rho + tan2 + tan2) / 6 XII = sec / nu5 * (5 + 28 * tan2 + 24 * tan4) / 120 XIIA = sec / nu7 * (61 + 662 * tan2 + 1320 * tan4 + 720 * tan6) / 5040 Ediff = (East - E0) : Ediff2 = Ediff * Ediff result.Latitude = (phi1 + Ediff2 * (-VII + Ediff2 * (VIII - IX * Ediff2))) / RADIAN result.Longitude = (lambda0 + Ediff * (X - XI * (Ediff2 + XII * ( Ediff2 - XIIA * Ediff2)))) / RADIAN Return result End Sub ' Conversion from WGS84/GRS80 ellipsoid To GB National Grid Public Sub WGS84ToOSGB(TRF As LatLon) As GridRef Dim result As GridRef result = TRFtoGrid(TRF, 6378137.000, 6356752.3141, -100000, 400000, 0.9996012717, 0.8552113335, -0.03490658504) Return result End Sub ' Conversion from GB National Grid to WGS84 lat/lon Public Sub OSGBToWGS84(Ref As GridRef) As LatLon Dim result As LatLon result = GridToTRF(Ref, 6378137.000, 6356752.3141, -100000, 400000, 0.9996012717, 0.8552113335, -0.03490658504) Return result End Sub